First, prepare the crust. Mix the flour, butter, sugar and salt in the bowl of a food processor until combined. Add the diced butter and pulse until butter pieces are the size of edamame. Add the egg and egg yolk and mix until the dough starts coming together. If the dough seems to lack moisture, add 1 tablespoon [15 ml] of very cold water and pulse again. Turn the dough out onto a work surface and gather it together in a large disk. Wrap in plastic and chill for 20 minutes before rolling.

Preheat the oven to 350ºF [175ºC]. Roll out the dough on a floured surface into a circle slightly bigger than your tart pan (preferably an 11-inch [28-cm] fluted pan). Put the dough into the pan and press the dough into the corners all the way around, and remove any overhanging dough from the sides. Patch any holes in the crust with the dough scraps.

Blind bake the pie crust: Line the tart shell with a large circle of parchment paper. Fill it with pie weights and bake in the preheated oven for 25 minutes. Remove from the oven, take out the pie weights and the paper together, and bake again for about 10 minutes, or until the bottom of the crust is cooked, but has not darkened. Let the crust cool while you prepare the filling. Leave the oven on.

Beat the butter and sugar together in an electric mixer fitted with the paddle attachment until light and fluffy, about 2 minutes. Add the eggs, beat for one more minute. Finally, beat in the flour, almonds, and almond extract, stopping to scrape the sides of the mixing bowl if necessary. Spread this mixture in an even layer into the baked tart shell. Begin arranging the sliced apples around the side in overlapping concentric circles, until the entire top of the tart is covered. Bake for about 30 minutes, or until the center of the tart is firm and fully cooked. Remove from the oven and cool completely before slicing.